Effect of Coefficient Rounding in Floating-Point Digital Filters

The effect of coefficient rounding in digital filters using floating-point arithmetic is analyzed. An error is defined as the difference between the output of a digital filter realized with a finite number of bits and the output of the same filter using infinite number of bits. It is shown that this error consists of two uncorrelated components. One component is due to the rounding of the arithmetic operations alone, and the other component represents the additional error due to coefficient rounding. Expressions are derived for the mean-square value of the error for the three canonical programming forms. The stability problem is studied by examining the shift of the pole locations due to the coefficient rounding. The mean-square value of the shift is calculated. Good agreement between theoretical and experimental results is obtained.